Table 3 places here, please.
Based on the frequentists approach showing non-significant regard to HRV, rumination, and depression, which thereby failed to reject the null hypothesis, Bayesian factor analyses (using JASP 0.16.3) were conducted to assess the likelihood of a correct null hypothesis (Quintana & Williams, 2018). Bayesian factor analysis is a development and alternative to testing the null hypotheses significance test. The Bayesian framework allows for the probabilistic description of parameters and hypotheses and can quantify the degree to which the data favors the null hypothesis (H0) or the alternative hypothesis (H1) (Gelman et al., 2014; McElreath, 2020). The H1 is that HRV is negatively correlated to rumination. The H0 rejects these correlations. In this study, we use Bayes factor 10 (BF10) which measures the degree to which H1 is supported by data compared with the H0. When the BF is higher than 1, the evidence is in favor of H1. The larger the factor, the higher the probability of the evidence in favor of H1. On the contrary, when the BF is less than 1, the evidence is in favor of H0. The smaller the factor, the higher the probability of the evidence in favor of H0.
Bayesian analysis showed that there was strong evidence supporting no correlations between HRV and RRStotal(BF10 = 0.152), Brooding (BF10 = 0.061), and Reflection (BF10 = 0.41), because the BF10 were less than 1.